Abstract This paper focuses on finite-order meromorphic solutions of nonlinear difference equation f n ( z ) + q ( z ) e Q ( z ) Δ c f ( z ) = p ( z ) {f}^{n}(z)+q(z){e}^{Q(z)}{\text{Δ}}_{c}f(z)=p(z) , where p , q , Q p,q,Q are polynomials, n ≥ 2 n\ge 2 is an integer, and Δ c f {\text{Δ}}_{c}f is the forward difference of f. A relationship between the growth and zero distribution of these solutions is obtained. Using this relationship, we obtain the form of these solutions of the aforementioned equation. Some examples are given to illustrate our results.

中文翻译：

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某些非线性差分方程的亚纯解

摘要 本文重点研究非线性差分方程 fn ( z ) + q ( z ) e Q ( z ) Δ cf ( z ) = p ( z ) {f}^{n}(z)+q 的有限阶亚纯解(z){e}^{Q(z)}{\text{Δ}}_{c}f(z)=p(z) ，其中 p , q , Q p,q,Q 是多项式，n ≥ 2 n\ge 2 是一个整数，Δ cf {\text{Δ}}_{c}f 是 f 的前向差。获得了这些解的增长和零分布之间的关系。使用这种关系，我们得到上述方程的这些解的形式。给出了一些例子来说明我们的结果。